Design of an ultrashort Si-nanowaveguide-based multimode interference coupler of arbitrary shape

A design procedure for an arbitrarily tapered multimode interference (MMI) coupler based on Si nanowaveguides is presented. First a series of the effective indices of the zeroth and first eigenmodes in multimode waveguides are obtained as the core width increases by using a full-vectorial finite-difference method. Two polynomial functions are used to fit the two relations between the effective indices and the core width. The phase difference Delta phi between the zeroth and first eigenmodes can then be easily calculated when the light goes through any given arbitrarily tapered MMI section. By making the phase difference Delta phi equal to a certain value Delta phi 0 required for an N-fold self-imaging, the length of a MMI coupler is determined. With the present design procedure, an ultrashort 2 x 2 parabolic MMI coupler is designed as an example. The size of the designed ultrashort MMI section is only approximately 1.4 microm x 4.7 microm.